This introductory textbook describes fundamental groups and their topological soul mates, the covering spaces. The author provides several illustrative examples that touch upon different areas of mathematics, but in keeping with the books introductory aim, they are all quite elementary. Basic concepts are clearly defined, proofs are complete, and no results from the exercises are assumed in the text.
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Editorial Reviews
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" ""A welcome addition to the library of basic topology."" - J. McCleary, Vassar College -J. McCleary, Vassar College, CHOICE Magazine, March 2004
""In addition to the lucid writing... and plentiful exercises, another nice feature of Lima's book is a number of references to the history of the ideas which he is presenting."" -Darren Glass, MAA Online , March 2004
""This is a book that all libraries should have, not because it is encyclopedic, but because it introduces the student to a variety of accessible applications and insights too quickly skimmed over in standard texts."" -Iain Aitchison, Australian Mathematical Society , November 2005
""Here is an excellent self-contained introduction to fundamental groups and covering spaces. It assumes only a few basic notions from topology . . . Though the book has a definite textbook feel to it, it provides an absorbing read for anyone interested in an introduction to algebraic topology. The text is interspersed with over 70 illustrative examples and over 50 well-drawn explanatory pictures. Overall, the book is clearly written and has a good flow to it and succeeds admirably in the task it set itself."" -Philip Maynard, The Mathematical Gazette , July 2004"
""In addition to the lucid writing... and plentiful exercises, another nice feature of Lima's book is a number of references to the history of the ideas which he is presenting."" -Darren Glass, MAA Online , March 2004
""This is a book that all libraries should have, not because it is encyclopedic, but because it introduces the student to a variety of accessible applications and insights too quickly skimmed over in standard texts."" -Iain Aitchison, Australian Mathematical Society , November 2005
""Here is an excellent self-contained introduction to fundamental groups and covering spaces. It assumes only a few basic notions from topology . . . Though the book has a definite textbook feel to it, it provides an absorbing read for anyone interested in an introduction to algebraic topology. The text is interspersed with over 70 illustrative examples and over 50 well-drawn explanatory pictures. Overall, the book is clearly written and has a good flow to it and succeeds admirably in the task it set itself."" -Philip Maynard, The Mathematical Gazette , July 2004"
About the Author
Elon Lages Lima is the Executive Director, Undergraduate Program in Business Administration and Economics at the Fundacao Getulio Vargas in Rio de Janeiro, Brazil. Lima received his M.S. and Ph.D. from the University of Chicago.
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Inside This Book
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First Sentence:
In this chapter, we introduce the basic notions about homotopy that will be used throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oriented double covering, free homotopic, orienting path, unique path lifting property, locally injective map, properly discontinuous group, distinguished neighborhood, locally trivial fibration, regular homotopy, topological group structure, local homeomorphism, same homotopy type, same rotation number, two continuous maps, closed differential form, path homotopy, antipodal map, conjugate class, free homotopy, convenient neighborhood, fundamental group, covering map, continuous multiplication, contractible space, local diffeomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Inverse Function New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
In this chapter, we introduce the basic notions about homotopy that will be used throughout the book. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
oriented double covering, free homotopic, orienting path, unique path lifting property, locally injective map, properly discontinuous group, distinguished neighborhood, locally trivial fibration, regular homotopy, topological group structure, local homeomorphism, same homotopy type, same rotation number, two continuous maps, closed differential form, path homotopy, antipodal map, conjugate class, free homotopy, convenient neighborhood, fundamental group, covering map, continuous multiplication, contractible space, local diffeomorphism Key Phrases - Capitalized Phrases (CAPs): (learn more)
Inverse Function New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 4
books:
- Foundations of Algebraic Topology (Mathematics Series) by Samuel Eilenberg in Back Matter
- Outside In by Karen Romano Young in Back Matter
- Algebraic Topology by Edwin H. Spanier in Back Matter
- Algebraic Topology: An Introduction (Graduate Texts in Mathematics) (v. 56) by William S. Massey in Back Matter
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